Unit 8: Circle Geometry Grade 9 Math Introduction ...
Unit 8: Circle Geometry
Introduction: Definitions
Grade 9 Math
Diameter
the distance across a circle, measured through its
center; or the line segment that joins two points on
the circle and passes through the center.
Radius
the distance or line segment from the center of a
circle to any point on the circle.
Chord(s)
a line segment that joins two points on a circle.
A
Arc
B
A segment of the circumference of a circle.
Minor Arc
The shorter of two arcs between two points on a circle.
For example: AB
Tangent
a line that intersects a circle at only one point.
Point of Tangency
the point where a tangent intersects a circle
Central Angle
An angle whose arms are radii of a circle.
Q
Inscribed Angle
An angle in a circle with its vertex and endpoints
of its arms on the circle.
P
R
For example,
PQR
Section 8.1 Properties of Tangents to a Circle
Tangent-Radius Property
A tangent to a circle is perpendicular to the radius
at the point of tangency.
APO = BPO = 900
Example Problems
A)
Point O is the center of a circle and AB is tangent to the circle. In
AOB = 550. Determine the measure of OBA.
Since
A = 900 and
OAB,
0 = 550
Then 90 + 55 = 145
The three angles in a triangle
add to 1800. So
145 = 350.
x = 180 ¨C
Try to find the missing angles in the following diagrams
A)
B)
x = 48o
x = 76o
Application Example
Since AC is a tangent ¡
BDA = BDC = 900
Find x
x + 90 + 57 = 180
x + 147 = 180
x + 147 - 147 = 180 - 147
x = 33o
Find y
y + 90 + 35 = 180
y + 125 = 180
y + 125 - 125 = 180 - 125
y = 55o
Using the Pythagorean Theorem in a Circle
1.
Since BM is a tangent we know
that OBM = 900.
a 2 + b 2 = c2
82 + b2 = 102
64 + b2 = 100
b2 = 100 ¨C 64
b2 = 36
b= ¡Ì36
b = 6 cm
Try this one!
2.
Since BM is a tangent we know
that OBM = 900.
a 2 + b 2 = c2
122 + b2 = 162
144 + b2 = 256
b2 = 256 ¨C 144
b2 = 112
b= ¡Ì112
b = 10.6 cm
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